The term 'remaster' is something that's used across multimedia as a whole, with the term holding significance when it comes to the likes of music and film. Remastering usually involves enhancing the quality of an original 'master' version, meaning the fabric of the source is merely enhanced, rather than modified.
Within videogames, this same rule usually applies, with the most popular form of remastering being based on fidelity and resolution. To put it simply, remastering an old game will make it look less like pixelated vomit on your fancy new TV.
Despite this simple definition, remasters can still vary in quality, which is often down to how much effort has gone into each instance. The
PlayStation 3 and
Xbox 360 saw a plethora of 'HD Remasters', mainly consisting of ported titles that weren't previously compatible on the aforementioned hardware. Other than upscaling the original title to an HD resolution, there's little else that distinguishes them from their original form.